i am solving a poisson equation with neumann boundary conditions: d^2[phi]/dx^2+d^2[phi]dy^2=S define: delta=d^2[phi]/dx^2+d^2[phi]dy^2-S after i obtained the solution, i computed delta(as defined) for the entire domain. is the solution still valid if the magnitude of one of the deltas reaches 0.02 as it should be far smaller than that(approaches 0)? any opinion or advice is welcomed. thanks regards, yfyap

(1). If the Left-hand side Is Equal to the Right-hand side, then obviously the solution is valid because it satisfies your equation. (2). If the Left-hand side Is Not Equal to the Right-hand side, then your definition of delta will be Non-zero. Thus, the equation is Not Satisfied. That also means you are not getting the right solution to satisfy your equation.

Dear YFYAP

This is not a simple question. My suggestions is: Check it with experimental data or another numerical results (another code or researcher).

2% error is maybe good enough for your case but it could be dramatic for the Challenger, that depends on your case's requirements.

You can have 0.01% error and your results can become useless becuase your definition of the RHS (ie. S in your eq.) do not match with the physical model that your case need.

Regards

Kike